The Edit Priorities button gives you some control over the order of payment options that customers see during checkout.
Note that you also can set the payment priority when you edit payment method rules. See To Edit Payment Method Rules
The Filter by Payment Module button temporarily shows or hides some payment methods, to make the Payment Method Rules tab a little less cluttered. It's similar to running a List Search.
For example, let's say that you have the following payment modules enabled in your store:
With these modules, you might have quite a few payment methods enabled. If you only want to view the Authorize.Net payment methods, click on the Filter by Payment Module button and select Authorize.Net. Note that you can also select more than one payment module at a time.
Module: The payment module that contains the current method.
Payment Method: The name of the payment method you are editing.
Priority: Priority lets you sort the order that payment methods are shown to customers during checkout. See Edit Priorities Button.
Display As: Change the name of this payment method as it is shown to customers during checkout.
Restrictions: Restrictions let you control when a payment method will be shown to customers.
Exclusions: Use the Exclusions drop-down list to remove a payment method during checkout based on the presence of another method. For example, you could prevent Visa and American Express from both being displayed during checkout at the same time:
To Use "Exclude This Method Unless Permitted by Products"
1.1. Go to > Payments > Payment Method Rules tab.
1.2. Double-click on a payment method to open the Payment Method Rules dialog box.
1.3. In the Payment Method Rules dialog box, check the "Exclude This Method Unless Permitted by Products" checkbox.
2.1 Go to > Catalog > Products tab > edit product > Product tab > Payment Rules section.
2.2 Select the check payment checkbox to allow it for the product you are editing. You would have to do this for every product where you want your customer to be able to pay by check. If you were going to enable the payment method for a large number of products, you can set the Permitted Payment Methods during export/import. See: > Data Management > Import/Export tab > Export Products to Flat File > Export Fields > Payment Rules Fields.
For an example of using "Limit Payment Methods" and "Permitted Payment Methods", please see To Disable Off-Line Payment Methods for Digital Products.